As indicated by the name, this is your character's house.
You can store items in it, and defend it with traps against robbers.
You can order traps in the back room of the fortress.
You only need a trap if you move from the novice quarter.
You can buy a bigger house in the palace.
Advanced houses have more advantage than only having more storage space:
There's a magical chair in them - using it will have varoius effects.
You can find a detailed description of the houses in the palace.